1. Field of the Invention
The present invention generally relates to computed tomography (CT) and, more particularly, to systems and methods for exact interior reconstruction using improved analytic continuation techniques and with the extension of such techniques to instant tomography and across other tomographic modalities.
2. Background Description
Classic CT theory targets exact reconstruction of a whole cross-section or of an entire object from complete projections, while practical applications such as medical CT, micro- and nano-CT often need to focus on a much smaller internal region of interest (ROI). Current CT theory cannot exactly reconstruct an internal ROI only from truncated projections associated with x-rays through the ROI because this interior problem does not have a unique solution. When applying traditional CT algorithms for interior reconstruction from truncated projection data, features outside the ROI may create artifacts overlapping inside features, rendering the images inaccurate or useless. Moreover, specific problems remain for pre-clinical imaging, as in the case of small animals (see Wang, G., “Micro-CT scanners for biomedical applications: an overview”, Adv. Imaging, 2001, 16: pp. 18-27). Although there has been an explosive growth in the development of cone-beam micro-CT scanners for small animal studies, the efforts are generally limited to cross-sectional or volumetric imaging at high spatial resolution of 20-100 μm at large radiation dose.
Traditional CT is necessarily associated with x-ray source and/or detector scanning so that projections can be collected from a sufficient number of orientations. Although the multi-source strategy has been a natural solution to higher temporal resolution CT and already used in the classic Mayo Clinic Dynamic Spatial Reconstructor (see Robb, R. A., et al, High-speed three-dimensional x-ray computed tomography: The dynamic spatial reconstructor. Proceedings of the IEEE, 1983. 71(3): p. 308-319, and Ritman, E. L., R. A. Robb, and L. D. Harris, Imaging physiological functions: experience with the DSR. 1985: philadelphia: praeger), the modern Siemens dual-source cone-beam scanner (see Flohr, T. G., et al, First performance evaluation of a dual-source CT (DSCT) system. European Radiology, 2006. 16(2): p. 256-268), and other systems, such an x-ray scanning mechanism remains indispensible. The bulkiness of sources/detectors in limited physical space has previously made it impossible to collect simultaneously a sufficient number of projections simultaneously.
The importance of performing exact image reconstruction from the minimum amount of data has been recognized since the introduction of CT scanning. A recent milestone was the two-step Hilbert transform method (see Noo et al. “A two-step Hilbert transform method for 2D image reconstruction”. Physics in Medicine and Biology, 2004. 49(17): p. 3903-3923), which was further expanded by Defrise et al. “Truncated Hilbert transform and image reconstruction from limited tomographic data.” Inverse Problems, 2006. 22(3): p. 1037-1053.
Despite the impressive advancement of the CT technology, there are still unmet, critical and immediate needs such as those mentioned above for better image quality at lower doses in many biomedical and other investigations.